The author's investigations in this area where largely motivated by Bourgain's book [1]} which states at the end of page 27: On the other hand, it would be most interesting to prove that analogue of (1.99) in low dimensions \(d=1,2\) . This is certainly a project of independent importance. Here (1.99) refers to the pointwise decay of the Schr̎odinger evolution proved by Journé, Soffer and Sogge [2]}, see the following section.
